When materials are compressed along a particular axis, they are most commonly observed to expand in directions transverse to the applied axial load. Conversely, most materials contract along a particular axis when a tensile load is applied along an axis transverse to the axis of contraction. The material property that characterizes this behavior is known as the Poisson's Ratio, which can be defined as the negative of the ratio of transverse/lateral strain to axial/longitudinal strain under axial loading conditions. The majority of materials are characterized by a positive Poisson's Ratio, which is approximately 0.5 for rubber, approximately 0.3 for aluminum, brass and steel, and approximately 0.2 for glass.
Materials with a negative Poisson's Ratio (NPR), on the other hand, will contract (or expand) in the transverse direction when compressed (or stretched) in the axial direction. Materials that exhibit negative Poisson's Ratio behavior are oftentimes referred to as “auxetic” materials. The results of many investigations suggest that auxetic behavior involves an interplay between the microstructure of the material and its deformation. Examples of this are provided by the discovery that metals with a cubic lattice, natural layered ceramics, ferroelectric polycrystalline ceramics, and zeolites may all exhibit negative Poisson's Ratio behavior. Moreover, several geometries and mechanisms have been proposed to achieve negative values for the Poisson's Ratio, including foams with reentrant structures, hierarchical laminates, polymeric and metallic foams. Negative Poisson's Ratio effects have also been demonstrated at the micrometer scale using complex materials which were fabricated using soft lithography and at the nanoscale with sheet assemblies of carbon nanotubes.
A significant challenge in the fabrication of auxetic materials is that it usually involves embedding structures with intricate geometries within a host matrix. As such, the manufacturing process has been a bottleneck in the practical development towards applications. A structure which forms the basis of many auxetic materials is that of a cellular solid. Research into the deformation of these materials is a relatively mature field with primary emphasis on the role of buckling phenomena, on load carrying capacity, and energy absorption under compressive loading. Very recently, the results of a combined experimental and numerical investigation demonstrated that mechanical instabilities in 2D periodic porous structures can trigger dramatic transformations of the original geometry. Specifically, uniaxial loading of a square array of circular holes in an elastomeric matrix is found to lead to a pattern of alternating mutually orthogonal ellipses while the array is under load. This results from an elastic instability above a critical value of the applied strain. The geometric reorganization observed at the instability is both reversible and repeatable and it occurs over a narrow range of the applied load. Moreover, it has been shown that the pattern transformation leads to unidirectional negative Poisson's Ratio behavior for the 2D structure, i.e., it only occurs under compression.
U.S. Pat. No. 5,233,828 (“'828 Patent”) shows an example of an engineered void structure—a combustor liner or “heat shield”—utilized in high temperature applications. Combustor liners are typically used in the combustion section of a gas turbine. Combustor liners can also be used in the exhaust section or in other sections or components of the gas turbine, such as the turbine blades. In operation, combustors burn gas at intensely high temperatures, such as around 3,000° F. or higher. To prevent this intense heat from damaging the combustor before it exits to a turbine, the combustor liner is provided in the interior of the combustor to insulate the surrounding engine. To minimize temperature and pressure differentials across a combustor liner, cooling feature have conventionally been provided, such as is shown in the '828 Patent, in the form of spaced cooling holes disposed in a continuous pattern. As another example, U.S. Pat. No. 8,066,482 B2 presents an engineered structural member having elliptically-shaped cooling holes to enhance the cooling of a desired region of a gas turbine while reducing stress levels in and around the cooling holes. European Patent No. EP 0971172 A1 likewise shows another example of a perforated liner used in a combustion zone of a gas turbine. None of the above patent documents, however, provide examples disclosed as exhibiting auxetic behavior or being engineered to provide NPR effects.
U.S. Patent Application Pub. No. 2010/0009120 A1 discloses various transformative periodic structures which include elastomeric or elasto-plastic periodic solids that experience transformation in the structural configuration upon application of a critical macroscopic stress or strain. Said transformation alters the geometric pattern, changing the spacing and the shape of the features within the transformative periodic structure. Upon removal of the critical macroscopic stress or strain, these elastomeric periodic solids recover their original form. By way of comparison, U.S. Patent Application Pub. No. 2011/0059291 A1 discloses structured porous materials, where the porous structure provides a tailored Poisson's ratio behavior. These porous structures consist of a pattern of elliptical or elliptical-like voids in an elastomeric sheet which is tailored, via the mechanics of the deformation of the voids and the mechanics of the deformation of the material, to provide a negative or a zero Poisson's ratio. All of the foregoing patent documents are incorporated herein by reference in their respective entireties and for all purposes.